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math252e - Math 252 Exam 1 Musial Musial Name_—_—...

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Unformatted text preview: Math 252 Exam 1 February 26, 2009 Musial Musial Name__—_—_ Instructions. Work each problem on the exam.. Where you are asked to solve an equation, make sure to find all solutions. Show all work. 1. Solve the DE. dy 1/2 =0. d2: 1+:r2 2. Solve the DE. 3/ + 32621] = $2. 3. Solve the DE and give the largest intervals on which a solution can exist: my' + y 2 622:. 4. A tank initially contains 300 gallons of saline solution with salinity 5 lbs of salt per gallon of solution. Solution having salinity 4 lbs of salt per gallon is pumped into the tank at a rate of 8 gallons per minute, and solution leaves the tank at the same rate of 8 gallons per minute. Find the function A (t) which models the amount of salt in the tank at any time, and find the amount if salt in the tank after a long time. Be sure to draw a picture. 5. Show that the differential form (m2+y2)dm+(y+my)dy=0 is not exact. Multiply both sides by the integrating factor 1 + as and verify that the resulting differential form is exact. Solve the DE. 6. For a series circuit containing only a resistor and an inductor, Kirchoff’s second law states that the sum of the voltage drop across the inductor (L (cit/(125)) and the voltage drop across the resistor (2R) is equal to the impressed voltage (E (t)) on the circuit. Suppose that a 12-volt battery is connected to an LR series circuit in which the induc~ tance is 0.2 henry and the resistance is 20 ohms. Determine the current 2' if the initial current is 0.5 amp. 7. Solve the IVP (w—y) dm+wdy=0,y(1) =1. 8. Solve the DE _d_y + y = e—zy2 d2: ' W131 {FM/ink 7C4“; 16/2001 Mvsl‘ofl 3) go/we X314g2elx 910% 3,0 Soluch/n Com eve/‘54» 0a (~00, 0) or ((5—9) 03—13 - Ll) FA‘P/ow: 89mm“ Ver'm‘l‘ K L(P°””/5 M30114” : 8572/ 3; 1L5 PW mm»? fiO‘i’MM j ouflvvfim_ ark“ £3 wha- \ffi/ goo ‘jA-o V0)U/y~0 diig‘u (U410h 4h hank (:e’Y‘OU‘tLS Cid/35W 300% ”Home (TA-MW 4 30 mm = 0.144%. w 4 sow—A)” ' ‘ A151 F mum» “ha/Ax 2< {00W - 3,4 24 Lb d A 1A ' f“ ,2 f. %”:‘A %3K:I~‘/Qau+ ’3}“ 11-3; / A/O) ;_§OOX5‘? ?OO ’25’ at (you (1.; AA 3; - 0w k7§f4 31 i, ’7 Cm; 2 19 Ag?“ , 32 ”7f— 8” *C i+ ’ Moo 6” +Q ,g { Pr: L100 4? C Q K K/ W_ WW» (ta/WSW} WM Sf/‘c/Q Ah): /§7}D 7. AIM: moo 4'200 Q V L “#21 5am law, may“ boo \LDS d%§‘l& ’3 I)’\ amt. —- )POFNI I“; (0A9 W imam/dig WM ’ l imp C. 3 Ala“ SID/V404) (’€ ,“7fl C13 max/37> r-I at R AmL Qacébyt @wg 3:0;th m‘fil'} Mxl} 49745417 C bu+ M/Y qty/M S/m/{lfi ”(9‘ 8%)” ”4”” 757% Mack-Q ‘ Q LHMJZ : € §.T’.;V‘7< .1 Mfr”) ca’twg‘D/VWHVPPM bfi’m 3;”; m»auwm—Am 5» (m ‘- (HmXél—ML) M + [lvkxfijpfiflowt 0 68+ a“ *3 *H‘fllB/‘w «k (mum +783) cm, 2» ejn/ ms) :67LY‘) Wepamwy, E 1 my. 3W My w L " 3w“: + fin—km) 3 .‘1 3. WW 9&3 § «Mm—i; W») 3 ‘1 1 1 7R Y X L §OIU4MM ’3‘ 4 \<th+— : 47/12, 4' 12— ; C C7\ 1:, ad? (004, Iva/MVP "’9 m %>‘7r-DL 51-M”§2 our ODE/3 W‘, \ (00+ ”’0 LQ ‘ $31) 6 #LC (ix 0 (o “(‘C €~\00f C(03:0 5‘: L5 (0 +C-(r) c= —0 l \ -(oole K: @(y*Cle v/ onlymwsa? , Cor/ea; loom M 4‘ NM WM“: ¢yz9ml WM édbsH-HJ-‘n‘m flit/x d417- UM$»X0L9\ {fxflu)‘) A“ + X/U/waum) :0 ‘XcM—{w& tXfiZngwsa :fl‘x + 78% =6 $8 XL 3:1 f __< Nick '1 jOU Cam/“{7L i Y M +€JM :15 ‘/%f‘®h’ mac/433% IKVOXL‘ X {1} '3 V“ (“4’44 AK 4— (J .1 C" 41o; u:<~/ém< jg x, C‘JFX C; %)< %[email protected] ‘=C ...
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